随着科学技术的发展和计算机技术的广泛应用，非线性方程组问题得到了数值研

With the development of science and technology and the widespread application of computer technology, the problem of nonlinear equations has received more and more attention from numerical researchers. In various aspects of production practice, science and technology, and life learning, non-linear relationships are ubiquitous relationships, and are also important topics in the field of optimization research. In order to make the nonlinear relationship better serve the society and be suitable for scientific research, the solution of the nonlinear equation system has been constantly sought, tried and innovated by scientists. <br>In recent years, many scholars have proposed many numerical methods for solving nonlinear equations. Among them, the more common method is the iterative method, including Newton iterative method and Ostrowski iterative method. This paper mainly studies the problem of solving nonlinear equations, improves the Newton method, and hopes to obtain higher order convergence. <br>The preface mainly introduces the research background and significance of solving nonlinear equations, and summarizes the research status of nonlinear equations at home and abroad. Finally, the work that this article will do is introduced. <br>The second chapter first introduces the knowledge of derivatives and median theorem, which is of great help to the use of differential median theorem to approximate third-order tensors in order to obtain higher convergence for solving equations. Then, the iterative method is introduced to solve nonlinear equations and convergence. <br>In Chapter 3, the Newton method is used to solve the system of nonlinear equations, and a method similar to the Newton iteration method is proposed. A two-step method based on the chebyshev method is also considered. The difference of the Jacobian matrix is ​​used to approximate the quadratic term, avoiding the third-order tensor Calculation and storage. At the same time, the local quadratic convergence under this method is maintained. <br>The fourth chapter is mainly to propose an algorithm of third-order convergence and to prove its convergence. <br>Chapter V, conducting numerical experiments .......

With the development of science and technology and the wide application of computer technology, the problem of nonlinear equation system has been paid more and more attention by numerical researchers. Non-linear relationship is a common relationship in production practice, science and technology and life learning, and it is also an important subject in the optimal research field. In order to make nonlinear relationships better serve society and be suitable for scientific research, the solution of nonlinear equations has been constantly sought, tried and innovated by scientists.<br>In recent years, many scholars have put forward many numerical methods to solve nonlinear equations, among which the more common method is iterative method, including Newton iterative method, Ostrowski iterative method and so on. In this paper, we mainly study the problem of solving nonlinear equations, improve the Newton method, and hope to get higher-order convergence.<br>The foreword mainly introduces the research background and significance of solving nonlinear equation symes, and summarizes the current situation of the solution of nonlinear equation symes at home and abroad. Finally, the paper introduces the work that will be done.<br>In the second chapter, the knowledge of derivative and median theorem is introduced first, which is of great help to the solution equation to obtain higher convergence, and to approximate the third-order tensor by differential median theorem. Then, it introduces the iterative method to solve the nonlinear equation system and the convergence.<br>In the third chapter, the nonlinear equation system is solved by Newton method, and a method similar to Newton's iterative method is proposed, and the two-step method based on chebyshev method is also considered, and the differential proximity of the Jacobite matrix is used to approximate the secondary term, thus avoiding the calculation and storage of the third-order cyanity. At the same time, the local secondary convergence under this method is maintained.<br>The fourth chapter, mainly put forward the third-order convergence algorithm, and its convergence to prove.<br>Chapter 5, carry out numerical experiments....

With the development of science and technology and the wide application of computer technology, more and more attention has been paid to the nonlinear equations. In production practice, science and technology, life learning and other aspects, the non-linear relationship is a universal relationship, but also an important topic in the field of optimization research. In order to make the non-linear relationship serve the society better and apply to scientific research, the solution of non-linear equations has been constantly sought, attempted and innovated by scientists.<br>In recent years, many scholars have put forward a lot of numerical methods for solving nonlinear equations, among which the more common method is iterative method, including Newton iterative method, Ostrowski iterative method and so on. In this paper, we mainly study the solution of nonlinear equations, improve Newton method, and hope to get higher order convergence.<br>The preface mainly introduces the research background and significance of solving nonlinear equations, and summarizes the research status of solving nonlinear equations at home and abroad. Finally, it introduces the work of this paper.<br>In the second chapter, we first introduce the knowledge of derivative and mean value theorem, which is very helpful to approximate the third-order tensor with differential mean value theorem in order to obtain higher convergence. Then, the iterative method for solving nonlinear equations and its convergence are introduced.<br>In the third chapter, Newton method is used to solve the nonlinear equations, and a method similar to Newton iterative method is proposed. Two steps based on Chebyshev method are also considered. The difference of Jacobian matrix is used to approximate the quadratic term, avoiding the calculation and storage of the third-order tensor. At the same time, the local quadratic convergence of the method is maintained.<br>In the fourth chapter, we propose the third-order convergence algorithm and prove its convergence.<br>In Chapter 5, numerical experiments are carried out<br>